" the water was spouting out of the top (the tank itself was virtually empty). Would an overflow outlet have stopped it?"
What you have described with the ball valve suggests that the plastic spout on top of the ball valve has broken or cracked. If this is so the valve you had fitted is known as a part 2 valve. I try to avoid fitting these in tanks as any downward pressure on a lid or cover could crack the spout.
In this situation I would usually fit what's known as a part 1 valve, these don't have a spout on top .. but an outlet underneath the valve.
What may have happened is the broken spout allowed the water flow to be directed out and over the side of the tank and on down through the house etc. I would expect an overflow to be fitted, but in this situation it wouldn't have helped.
The sort of thing that would cause the spout to snap is pressure directed from above via a poor quality lid or cover ... I've usually found pigeons, birds or squirrels the most likely culprits.
... the other culprit is the one who made the poor quality cover (usually constructed from a few battens a sheet of polystyrene and a bit of polythene).